Question: Calculate the quotient below and give your answer in scientific notation. ${\dfrac{1.72\times 10^{0}}{4.0\times 10^{-3}}} =\ ?$
Explanation: Start by collecting the significands and exponents. $ {\dfrac {{1.72} \times {10^{0}}} {{4.0} \times {10^{-3}}} = {\dfrac{1.72}{4.0}} \times {\dfrac{10^{0}}{10^{-3}}}} $ Then divide each term separately. When dividing exponents with the same base, subtract their powers. $= {0.43} \times {10^{0 \,-\, -3}}$ $= {0.43} \times {10^{3}}$ To write the answer correctly in scientific notation, the first number needs to be between $1$ and $10$. In this case, we need to move the decimal one position to the right without changing the value of our answer. We can use the fact that ${0.43}$ is the same as ${4.3 \div 10}$, or ${4.3 \times 10^{-1}}$. $ = {4.3 \times 10^{-1}} \times {10^{3}} $ $ = 4.3 \times 10^{{-1} + {3}} $ $= 4.3\times 10^{2}$